In the article Application of Statistical Design in the Leaching Study of Low-Grade Manganese Ore Using Aqueous Sulfur Dioxide (P. Naik, L. Sukla, and S. Das, Separation Science and Technology, 2002:13751389), a fitted model for predicting the extraction of manganese in % (y) from particle size in mm (x1), the amount of sulfur dioxide in multiples of the stoichiometric quantity needed for the dissolution of manganese (x2), and the duration of leaching in minutes (x3) is given as y = 56.145 9.046x1 33.421x2 + 0.243x3 0.5963x1 x2 0.0394x1 x3 + 0.6022x2 x3 + 0.6901x 2 1 + 11.7244x 2 2 0.0097x 2 3 There were a total of n = 27 observations, with SSE = 209.55 and SST = 6777.5. a. Predict the extraction percent when the particle size is 3 mm, the amount of sulfur dioxide is 1.5, and the duration of leaching is 20 minutes.
b. Is it possible to predict the change in extraction percent when the duration of leaching increases by one minute? If so, find the predicted change. If not, explain why not.
c. Compute the coefficient of determination R2 .
d. Compute the F statistic for testing the null hypothesis that all the coefficients are equal to 0. Can this hypothesis be rejected?